Plasma Interactions with Electromagnetic Fieldscedarweb.vsp.ucar.edu/wiki/images/8/87/Ionosphere_EM... · 2015-06-20 · Plasma Interactions with Electromagnetic Fields Roger H. Varney
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Plasma Interactions with Electromagnetic Fields
Roger H. Varney
SRI International
June 21, 2015
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 1 / 23
1 Introduction
2 Particle Motion in Fields
3 Generation of Electric Fields in PlasmasAmbipolar Electric FieldsDynamo TheoryElectrodynamical Magnetosphere-Ionosphere Coupling
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 2 / 23
Introduction
The Ionosphere and Thermosphere
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 3 / 23
Introduction
Magnetic Structure of the Ionosphere and Magnetosphere
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 4 / 23
Particle Motion in Fields
Particle Motion in a Uniform B field
mdv
dt= qv × B
Separate by components
mdvx
dt= qvyBz
mdvy
dt= −qvxBz
Solution to coupled system with v0 = v0x
vx = v0 cos (Ωt)
vy = −sgn (q)v0 sin (Ωt)
Gyrofrequency: Ω = |qB|m
x
y
z
B = Bz z
Electrons
Ions
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 5 / 23
Particle Motion in Fields
The E× B Drift
VD
B
E
vD =E× B
B2
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 6 / 23
Particle Motion in Fields
Electric Fields in Different Frames of Reference
Lorentz Force: F = q [E+ v × B]
In a different frame of reference moving with velocity u
F′ = q[E′ + (v − u)× B
]
The force must be the same in all reference frames: F = F′
E′ = E+ u× B
The frame moving at the E× B drift velocity is special:
E′ = E+E× B
B2× B
= E−E⊥B
2
B2
= 0 Assuming: E‖ = 0
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 7 / 23
Generation of Electric Fields in Plasmas Ambipolar Electric Fields
Ambipolar Electric Fields and Ambipolar Diffusion
Steady state parallel electron momentum equation:
me
[∂
∂t(neue) +∇‖ ·
(neu
2e
)]
= −∇‖pe − neeE‖ −→ E‖ = −1
ene∇‖pe
Substitute into parallel ion momentum equation:
mi
[∂
∂t(niui) +∇‖ ·
(niu
2i
)]
= −∇‖pi −ni
ne∇‖pe −minig‖
−mini∑
j
νij (ui − uj)+
+
+
+
+
-
-
-
-
-
ER. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 8 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Fundamentals of Ionospheric Electrodynamics
Electrostatic Limit of Maxwell’s Equations:
∇× B = µ0J+
01
c2∂E
∂t−→ ∇ · J = 0
∇× E = −0
∂B
∂t−→ E = −∇Φ
Ohm’s Law for the ionosphere:
J = σ · E+ J0
Putting everything together yields a boundary value problem:
∇ · σ · ∇Φ = ∇ · J0
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 9 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Ohm’s Law for the Ionosphere
Steady-state momentum equation for each species (zero neutral windcase):
0 = nαqα (E+ uα × B)− ναnmαnαuα
Resulting Ohm’s Law:
J =∑
α
nαqαuα −→ J =
σP −σH 0σH σP 00 0 σ0
· E
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 10 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Conductivity Profiles
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 11 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Other Kinds of Current
Substitute F for qαE in steady state momentum equation.
Wind drag: F = ναnmαun −→ J = σ · (un × B)
Gravity: F = mαg −→ J = Γ · g
Pressure Gradients (Diamagnetic Currents):F = − 1
nα∇pα −→ J = D · ∇
∑
αpα
Complete Dynamo Equation:
∇ · σ · ∇Φ = ∇ ·
(
σ · (un × B) + Γ · g+D · ∇∑
α
pα
)
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 12 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Slab Model of the F-region Dynamo
J = σP (E+ un × B)
Two ways to achieve ∇ · J = 01 Parallel currents which close elsewhere2 J = 0
J = 0 −→ E = −un × B
VD =E× B
B2=
−un ×B× B
B2= un
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 13 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Slab Model of the E-region Dynamo
Suppose Ex is the eastward component of un × B in the E-region.
A vertical electric field forms to oppose the vertical Hall current.
σHEx = σPEz =⇒ Ez =σHσP
Ex
The Hall current from this new Ez adds to the existing Pedersen currentfrom Ex
Jx = σHEz + σPEx =[(σH/σP)
2 + 1]σPEx ≡ σCEx
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 14 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Equatorial Fountain Effect
−20 −10 0 10 20 30 400
500
1000
Latitude
Alti
tudeNe (cm−3)
3
4
5
6
7
00 06 12 18 00 06 12 18 00−20
0
20
Ver
tical
Drif
t (m
/s)
Local Time
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 15 / 23
Generation of Electric Fields in Plasmas Dynamo Theory
Influences of Atmospheric Tides (Immel et al. 2006)
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 16 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
Current Systems in the Ionosphere and Magnetosphere
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 17 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
Closure of Field Aligned Currents in a Slab Ionosphere
3D potential equation with magnetospheric currents:
∇ · σ · ∇Φ = ∇ · Jmag
Integrate over altitude, assume equipotential field lines:
∇⊥ · Σ · ∇⊥Φ =
∫
∇ · Jmag dz
Expand the divergence:
∇ · Jmag = ∇⊥ · J⊥ +∂J‖
∂z
J⊥ goes to 0 above ionosphere, thus:∫
∇ · Jmag dz = J‖
2D slab ionosphere potential equation:
∇⊥ · Σ · ∇⊥Φ = J‖
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 18 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
High Latitude Convection Patterns
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 19 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
Energy Transport: Poynting’s Theorem
Poynting’s Theorem:
∂
∂t
[
ǫ0 |E|2
2+
|B|2
2µ0
]
︸ ︷︷ ︸
Energy Density
+∇ ·
[E× B
µ0
]
︸ ︷︷ ︸
Energy Flux
= −J · E︸ ︷︷ ︸
Joule Heating
Ionospheric Joule Heating: Use E field in the neutral wind frame
J · E′ =(σ · E′
)· E′
= σP |E+ un × B|2
= nimiνin |ui − un|2
See Appendix A of Thayer and Semeter, 2004, JASTP.
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 20 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
Joule Heating
Weimer, 2005.
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 21 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
Conductivity Effects on Magnetosphere (Lotko et al., 2014)
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 22 / 23
Generation of Electric Fields in Plasmas Electrodynamical Magnetosphere-Ionosphere Coupling
Summary of Ionospheric Electrodynamics
∇ · σ · ∇Φ = ∇ ·
(
σ · (un × B) + Γ · g+D · ∇∑
α
pα + Jmag
)
The ionospheric potential, and thus the E× B drifts, depend on:
Neutral winds (driving from below)
Magnetospheric currents (driving from above)
Ionospheric conductivities (chemistry)
Ionospheric pressure gradients (energetics)
R. H. Varney (SRI) Plasmas and EM Fields June 21, 2015 23 / 23
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